Xamarin was started as an experiment to try and develop a version of .NET for Linux in early 2000, and was first known as an open source project called Mono.
Later, the same project was developed and supported by a new company called Xamarin, which was created by the very first developers of Mono, and was also known as MonoTouch and Mono for Android.
Development of Mono continued and it was later renamed Xamarin, which supported Android and iOS app development.
Xamarin has now been acquired by Microsoft and is developed and supported as one of the products offered by Microsoft with great integration with the existing IDE, Visual Studio, and it even has its own IDE, called Xamarin Studio, which is available for both Mac and Windows.
